Soweto residents are looking for a political solution to their ongoing electricity problems, which have resulted in large parts of the township being plunged into darkness due to illegal connections, collapsing infrastructure and ballooning household debt to Eskom.

On Tuesday, hundreds of residents of the biggest township in the country took their frustrations over prolonged blackouts due to the explosion of overloaded substations and a culture of nonpayment to the mayor of Johannesburg, Mpho Phalatse’s doorstep in Braamfontein...